Casting the copy of the prepared spell works just like casting any other spell. You have to pay its cost, and you have to follow the timing rules put in place by its card type. If it's a sorcery like Rampant Growth, you can cast it during your main phase if the stack is empty. If you cast a prepare spell from exile, the prepared creature becomes unprepared, meaning it loses the prepared designation.

The ability word opus highlights triggered abilities that trigger whenever you cast an instant or sorcery spell. Each opus ability has an initial effect and an additional or alternative effect if you spent five or more mana to cast the spell that caused the opus ability to trigger.

You may cast a card with flashback from your graveyard. If you do, you pay its flashback cost rather than paying its mana cost. Flashback doesn't change when you can cast the spell, so a sorcery with flashback can still only be cast during your main phase. Also, casting a spell with flashback doesn't change its mana value. Mana value is always based on a spell's mana cost, even if you pay an alternative cost to cast it.

Paradigm is a new keyword that appears on a cycle of sorceries and gives them true staying power. The first time a particular spell with paradigm resolves for you, you exile it. From that point forward, at the beginning of each of your first main phases, you may cast a copy of it without paying its mana cost. Casting each of these copies is optional, and you'll have the opportunity to cast one on each of your turns no matter what happens to the previous ones.